Foundations of Science

, Volume 23, Issue 3, pp 443–474 | Cite as

How Future Depends on Past and Rare Events in Systems of Life

  • Giuseppe Longo


The dependence on history of both present and future dynamics of life is a common intuition in biology and in humanities. Historicity will be understood in terms of changes of the space of possibilities (or of “phase space”) as well as by the role of diversity in life’s structural stability and of rare events in history formation. We hint to a rigorous analysis of “path dependence” in terms of invariants and invariance preserving transformations, as it may be found also in physics, while departing from the physico-mathematical analyses. The idea is that the (relative or historicized) invariant traces of the past under organismal or ecosystemic transformations contribute to the understanding (or the “theoretical determination”) of present and future states of affairs. This yields a peculiar form of unpredictability (or randomness) in biology, at the core of novelty formation: the changes of observables and pertinent parameters may depend also on past events. In particular, in relation to the properties of synchronic measurement in physics, the relevance of diachronic measurement in biology is highlighted. This analysis may a fortiori apply to cognitive and historical human dynamics, while allowing to investigate some general properties of historicity in biology.


Biological Evolution Space of Possible Phenotypes Invariance Processual Time Historical Time 



Claus Halberg and the referees made several insightful and constructive comments.


(Papers (co-)authored by Longo are downloadable from:

  1. Amsterdamski, S., et al. (Eds.). (1990). La querelle du déterminisme. Paris: Gallimard.Google Scholar
  2. Arndt, M., Juffmann, T., & Vedral, V. (2009). Quantum physics meets biology. HFSP Journal, 3(6), 386–400.CrossRefGoogle Scholar
  3. Arnold, V.-I. (1992). Catastrophe theory (3rd ed.). Berlin: Springer.CrossRefGoogle Scholar
  4. Aspect, A., Grangier, P., & Roger, G. (1982). Experimental realization of the Einstein–Podolsky–Rosen–Bohm Gedanken experiment: A new violation of Bell’s inequalities. Physical Review Letters, 49, 91.CrossRefGoogle Scholar
  5. Bailly, F., & Longo, G. (2009). Biological organization and anti-entropy. Journal of Biological Systems, 17, 63–96.CrossRefGoogle Scholar
  6. Bailly, F., & Longo, G. (2011). Mathematics and the natural sciences; The Physical Singularity of Life. London: Imperial College Press (original French version, Hermann, 2006).Google Scholar
  7. Bécavin, C., Victor, J. M., & Lesne, A. (2012). The condensed chromatin fiber: An allosteric chemo-mechanical machine for signal transduction and genome processing. Physical Biology, 9, 013001.CrossRefGoogle Scholar
  8. Berry, M. (1990). Anticipations of geometric phase. Physics Today, 43(12), 34–40.CrossRefGoogle Scholar
  9. Berthoz, A. (2000). The brain sense of movement. Cambridge, MA: Harvard University Press.Google Scholar
  10. Bertini, L., De Sole, A., Gabrielli, D., Jona-Lasinio, G., & Landim, C. (2015). Macroscopic fluctuation theory. arXiv:1404.6466 [cond-mat.stat-mech].
  11. Binney, J., Dowrick, N. J., Fisher, A. J., & Newman, M. E. J. (1992). The theory of critical phenomena: An introduction to the renormalization group. Oxford: Oxford University Press.Google Scholar
  12. Bizzarri, M. (2012). The New Alchemist. The risks of genetic modification. Boston: WIT Press.Google Scholar
  13. Blount, Z. D., Borland, C. Z., & Lenski, R. E. (2008). Historical contingency and the evolution of a key innovation in an experimental population of Escherichia coli. Proceedings of the National Academy of Sciences of the United States of America, 105, 7899–7906.CrossRefGoogle Scholar
  14. Botzung, A., Denkova, E., & Manning, L. (2008). Experiencing and future personal events: Functional neuroimaging on the neural bases of mental time travel. Brain and Cognition, 66(2), 202–212.CrossRefGoogle Scholar
  15. Brentari, C. (2015). Jakob von Uexküll: The discovery of the Umwelt between biosemiotics and theoretical biology. Berlin: Springer.CrossRefGoogle Scholar
  16. Buiatti, M., & Longo, G. (2013). Randomness and multi-level interactions in biology. Theory in Biosciences, 132(3), 139–158.CrossRefGoogle Scholar
  17. Calude, C. (2002). Information and randomness (2nd ed.). Berlin: Springer.CrossRefGoogle Scholar
  18. Calude, C., & Longo, G. (2015). Classical, quantum and biological randomness as relative incomputability. Natural Computing, 15(2), 263–278.CrossRefGoogle Scholar
  19. Chibbaro, S., Rondoni, L., & Vulpiani, A. (2014). Reductionism, emergence and levels of reality. Berlin: Springer.CrossRefGoogle Scholar
  20. Chouard, T. (2010). Evolution: Revenge of the hopeful monster. Nature, 463, 864–867.CrossRefGoogle Scholar
  21. Connes, A. (1994). Non-commutative geometry. New York: Academic Press.Google Scholar
  22. de Souza, F., Franchini, L., & Rubistein, M. (2013). Exaptation of transposable elements into novel cis-regulatory elements: Is the evidence always strong? Molecular Biology and Evolution, 30(6), 1239–1251.CrossRefGoogle Scholar
  23. Deacon, T. (2011). Incomplete nature: How mind emerged from matter. New York: W.W. Norton & Company.Google Scholar
  24. Deacon, T. (2015). Steps to a science of biosemiotics. Green Letters: Studies in Ecocriticisms, 19(3). doi: 10.1080/14688417.2015.1072948.
  25. Desprat, N., Supatto, W., Pouille, P.-A., Beaurepaire, E., & Farge, E. (2008). Tissue deformation modulates twist expression to determine anterior midgut differentiation in Drosophila embryos. Developmental Cell, 15(3), 470–477.CrossRefGoogle Scholar
  26. Devaney, R. L. (1989). An introduction to chaotic dynamical systems. Reading, MA: Addison-Wesley.Google Scholar
  27. Disertori, M., Sabot, C., & Tarrès, P. (2015). Transience of edge-reinforced random walk. Communications in Mathematical Physics, 339(1), 121–148.CrossRefGoogle Scholar
  28. Duncan, A. W. (2013). Aneuploidy, polyploidy and ploidy reversal in the liver. Seminars in Cell & Developmental Biology, 24(4), 347–356.CrossRefGoogle Scholar
  29. Edelman, G. (1990). The remembered present: A biological theory of consciousness. New York: Basic Books.Google Scholar
  30. Edelman, G. M., & Gally, J. A. (2001). Degeneracy and complexity in biological systems. Proceedings of the National Academy of Science, 24, 13763–13768.CrossRefGoogle Scholar
  31. Edelman, G., & Tononi, G. (2000). A universe of consciousness. How matter becomes immagination. London: Basic Books.Google Scholar
  32. Einstein, A., Podolsky, B., & Rosen, N. (1935). Can quantum-mechanical description of physical reality be considered complete? Physical Review, 41, 777.CrossRefGoogle Scholar
  33. Felin, T., Kauffman, S., Koppl, R., & Longo, G. (2014). Economic opportunity and evolution: Beyond bounded rationality and phase space. Strategic Entrepreneurship Journal, 8(4), 269–282.CrossRefGoogle Scholar
  34. Fernandez-Sanchez, M.-E., Serman, F., Ahmadi, P., & Farge, E. (2010). Mechanical induction in embryonic development and tumor growth integrative cues through molecular to multicellular interplay and evolutionary perspectives. Methods in Cell Biology, 98(10), 295–321.CrossRefGoogle Scholar
  35. Gil, F. (1981). Il tempo del pensiero. In Le frontiere del tempo (Romano ed.). Milano: Il Saggiatore.Google Scholar
  36. Gogarten, J. P., & Townsend, J. P. (2005). Horizontal gene transfer, genome innovation and evolution. Nature Reviews Microbiology, 3(9), 679–687.CrossRefGoogle Scholar
  37. Goldenfeld, N., & Woese, C. (2011). Life is physics: Evolution as a collective phenomenon far from equilibrium. Annual Review of Condensed Matter Physics, 2, 375–399.CrossRefGoogle Scholar
  38. Gould, S.-J. (1989). Wonderful life. New York: Norton & Co.Google Scholar
  39. Gould, S. J. (1996). Full house. New York: Three Rivers Press.CrossRefGoogle Scholar
  40. Gould, S.-J. (2002). The structure of evolutionary theory. Cambridge, MA: Harvard University Press.Google Scholar
  41. Gould, S.-J., & Vrba, E. (1982). Exaptation—A missing term in the science of form. Paleobiology, 8, 4–15.CrossRefGoogle Scholar
  42. Grafen, A. (1982). The formal darwinism project in outline. Biology and Philosophy. doi: 10.1007/s10539-013-9414.Google Scholar
  43. Grant, B., & Grant, P. (1993). Evolution of Darwin’s finches caused by a rare climatic event. Proceedings of the Royal Society of London B: Biological Sciences, 251, 111–117.CrossRefGoogle Scholar
  44. Harms, M., & Thornton, J. (2014). Historical contingency and its biophysical basis in glucocorticoid receptor evolution. Nature, 512, 203–207.CrossRefGoogle Scholar
  45. Hurtado, P. I., Lasanta, A., & Prados, A. (2013). Typical and rare fluctuations in nonlinear driven diffusive systems with dissipation. Physical Review E, 88, 022110.CrossRefGoogle Scholar
  46. Huxley, J. (1943). Evolution, the modern synthesis. New York: Harper and Brothers Publishers.Google Scholar
  47. Islam, J. N. (2001). An introduction to mathematical cosmology. Cambridge, MA: Cambridge University Press.CrossRefGoogle Scholar
  48. Jablonka, E., & Lamb, M. J. (1998). Epigenetic inheritance in evolution. Journal of Evolutionary Biology, 11(2), 159–183.CrossRefGoogle Scholar
  49. Jablonka, E., & Lamb, M. J. (2008). Evolution in four dimensions. Cambridge, MA: MIT Press.Google Scholar
  50. Jacob, P. (1981). Le Jeu des possibles, essai sur la diversité du vivant. Paris: Fayard.Google Scholar
  51. Kauffman, S. A. (2002). Investigations. Oxford: Oxford University Press.Google Scholar
  52. Keeling, P. J., & Palmer, J. D. (2008). Horizontal gene transfer in eukaryotic evolution. Nature Reviews Genetics, 9(8), 605–618.CrossRefGoogle Scholar
  53. Kogan, O. (2014). Onset of singularities in the pattern of fluctuational paths of a nonequilibrium system., (see also
  54. Koppl, R., Kauffman, S., Longo, G., & Felin, T. (2015). Economy for a creative world. Journal of Institutional Economics, 11(01), 1–31.CrossRefGoogle Scholar
  55. Kosmann-Schwarzbach, Y. (2010). The Noether theorems: Invariance and conservation laws in the twentieth century. Berlin: Springer.Google Scholar
  56. Laskar, J. (1994). Large scale chaos in the solar system. Astronomy and Astrophysics, 287, L9–L12.Google Scholar
  57. Lemke, H., Coutinho, A., & Lange, H. (2004). Lamarckian inheritance by somatically acquired maternal IgG phenotypes. Trends in Immunology, 25(4), 180–186.CrossRefGoogle Scholar
  58. Lesne, A. (2008). Robustness: Confronting lessons from physics and biology. Biological Reviews of the Cambridge Philosophical Society, 83(4), 509–532.Google Scholar
  59. Longair, M. (2006). The cosmic century: A history of astrophysics and cosmology. Cambridge, MA: Cambridge University Press.CrossRefGoogle Scholar
  60. Longo, G. (2010). Interfaces of incompleteness. In Italian version in La Matematica (Vol. 4). Torino: Einuadi (downloadable in English).Google Scholar
  61. Longo, G. (2015). Conceptual analyses from a Grothendieckian perspective: Reflections on synthetic philosophy of contemporary mathematics by Fernando Zalamea. In Speculations, December 2015.
  62. Longo, G., & Montévil, M. (2014). Perspectives on organisms: Biological time, symmetries and singularities. Dordrecht: Springer.CrossRefGoogle Scholar
  63. Longo, G., & Montévil, M. (2017). Models vs. simulations: A comparison by their theoretical symmetries. In L. Magnani & T. Bertolotti. (Eds.), Springer handbook of model-based science. Berlin: Springer.Google Scholar
  64. Longo, G., Montévil, M., & Kauffman, S. (2012). No entailing laws, but enablement in the evolution of the biosphere. In Invited Paper, proceedings of the genetic and evolutionary computation conference, GECCO’12. Philadelphia, PA: ACM.Google Scholar
  65. Longo, G., Montévil, M., Sonnenschein, C., & Soto, A. (2015). In search of principles for a theory of organisms. Journal of Biosciences, 40(5), 955–968.Google Scholar
  66. Longo, G., & Mugur-Schachter, M. (Eds.) (2014). Developments of the concepts of randomness, statistic, and probability. In Mathematical structures in computer science (Vol. 24(3)). Cambridge University Press.Google Scholar
  67. Longo, G., & Perret, N. (2017). Contributions to a theory of biological time: Anticipation, protention and biological inertia. In E. Ippoliti (Ed.), Building theories, sciences and hypotheses. Berlin: Springer.Google Scholar
  68. Marinucci, A. (2017). From deterministic biology to relational biology, (submitted).Google Scholar
  69. Miquel, P. A. (2015). Sur le concept de nature. Paris: Hermann.Google Scholar
  70. Misslin, R. (2003–2004). Une vie de cellule. Forme et espace. Dans “Géométrie et Cognition”. In Longo, G. (Ed.), Numéro spécial de la Revue de Synthèse, Editions de la rue d’Ulm, tome (p. 124).Google Scholar
  71. Montévil, M., & Mossio, M. (2015). Closure of constraints in biological organisation. Journal of Theoretical Biology, 372, 179–191.CrossRefGoogle Scholar
  72. Moreno, A., & Mossio, M. (2015). Biological autonomy, a philosophical and theoretical enquire. Berlin: Springer.Google Scholar
  73. Needham, J. (1951). Human laws and the laws of nature in China and the West. Journal of the History of Ideas, XII(3–32), 194–231.CrossRefGoogle Scholar
  74. Nicolis, G., & Prigogine, I. (1977). Self-organization in non-equilibrium systems. New York: Wiley.Google Scholar
  75. Nowacki, M., & Landweber, L. F. (2009). Epigenetic inheritance in ciliates. Current Opinion in Microbiology, 12(6), 638–643.CrossRefGoogle Scholar
  76. Paaby, A., & Rockma, M. (2014). Cryptic genetic variation: Evolution’s hidden substrate. Nature Reviews Genetics, 15, 247–258.CrossRefGoogle Scholar
  77. Pal, C., Papp, B., & Lercher, M. J. (2005). Adaptive evolution of bacterial metabolic networks by horizontal gene transfer. Nature Genetics, 37(12), 1372–1375.CrossRefGoogle Scholar
  78. Plankar, M., Jerman, I., & Krasovec, R. (2011). On the origin of cancer: Can we ignore coherence? Progress in Biophysics and Molecular Biology, 106, 2.CrossRefGoogle Scholar
  79. Prochiantz, A. (1997). Les anatomies de la pensee. Paris: Odile Jacob.Google Scholar
  80. Rando, O. J., & Verstrepen, K. J. (2007). Timescales of genetic and epigenetic inheritance. Cell, 128(4), 655–668.CrossRefGoogle Scholar
  81. Roux, S. (2009). Controversies on legality (1680–1710). In L. Daston & M. Stolleis (Eds.), Natural law and laws of nature in early modern Europe (pp. 199–214). Aldershot: Ashgate Publishing.Google Scholar
  82. Rowan, S., Hough, J., & Crooks, D. (2005). Thermal noise and material issues for gravitational wave detectors. Physics Letters A, 347(1–3), 25–32.CrossRefGoogle Scholar
  83. Schwartz, L. (1951). Théorie des distributions (Vol. 1–2). Paris: Hermann.Google Scholar
  84. Sethna, J. P. (2006). Statistical mechanics: Entropy, order parameters, and complexity. New York: Oxford University Press.Google Scholar
  85. Shomrat, T., & Levin, M. (2013). An automated training paradigm reveals long-term memory in planarians and its persistence through head regeneration. The Journal of Experimental Biology, 216, 3799–3810.CrossRefGoogle Scholar
  86. Soto, A., & Longo, G. (Eds.) (2016). A theory of organisms. In Special issue of Progress in biophysics and molecular biology. Elsevier. doi: 10.1016/j.pbiomolbio.2016.
  87. Szpunar, K., Watson, J., & McDermott, K. (2007). Neural substrates of envisioning the future. Proceedings of the National Academy of Sciences, 104(2), 643–647.CrossRefGoogle Scholar
  88. Torday, J.-S. (2015). What we talk about when we talk about evolution. Cell Communication Insights, 7, 1–15.CrossRefGoogle Scholar
  89. Uzan, J.-P. (2011). Varying constants, gravitation and cosmology. Living Reviews in Relativity, 14(2), 1–155.Google Scholar
  90. Venditti, C., Meade, A., & Pagel, M. (2010). Phylogenies reveal new interpretation of speciation and the Red Queen. Nature, 463, 349–352.CrossRefGoogle Scholar
  91. Vulpiani, A., Cecconi, F., Cencini, M., Puglisi, A., & Vergni, D. (Eds.). (2014). Large deviations in physics. Berlin: Springer.Google Scholar
  92. West-Eberhard, M.-J. (2003). Developmental plasticity and evolution. New York: Oxford University Press.Google Scholar
  93. West-Eberhard, M.-J. (2005). Developmental plasticity and the origin of species differences. Proceedings of the National Academy of Sciences, 102(Suppl. 1), 6543–6549.CrossRefGoogle Scholar
  94. Weyl, H. (1949). Philosophy of mathematics and of natural sciences. Princeton, NJ: Princeton University Press.Google Scholar
  95. Zalamea, F. (2012). Synthetic philosophy of contemporary mathematics. NY: Urbanomic and Sequence Press.Google Scholar
  96. Zenik, Y., Solomon, S., & Yaari, G. (2015). Species survival emerge from rare events of individual migration. Nature Scientific Reports, 5, 7877. doi: 10.1038/srep07877.

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© Springer Science+Business Media B.V. 2017

Authors and Affiliations

  1. 1.Centre Cavaillès, République des Savoirs, CNRSCollège de France et Ecole Normale SupérieureParisFrance
  2. 2.Department of Integrative Physiology and PathobiologyTufts University School of MedicineBostonUSA

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